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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(cos(x)+sin(2*x)+sin(1/(x^2)))+sin(1/(x^2))

¿Cómo vas a descomponer esta sqrt(cos(x)+sin(2*x)+sin(1/(x^2)))+sin(1/(x^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     _____________________________          
    /                        /1 \       /1 \
   /  cos(x) + sin(2*x) + sin|--|  + sin|--|
  /                          | 2|       | 2|
\/                           \x /       \x /
(sin⁡(2x)+cos⁡(x))+sin⁡(1x2)+sin⁡(1x2)\sqrt{\left(\sin{\left(2 x \right)} + \cos{\left(x \right)}\right) + \sin{\left(\frac{1}{x^{2}} \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(2*x) + sin(1/(x^2))) + sin(1/(x^2))
Simplificación general [src] 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Respuesta numérica [src] 
(cos(x) + sin(1/(x^2)) + sin(2*x))^0.5 + sin(1/(x^2))
(cos(x) + sin(1/(x^2)) + sin(2*x))^0.5 + sin(1/(x^2))
Unión de expresiones racionales [src] 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Denominador común [src] 
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    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Combinatoria [src] 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Potencias [src] 
        __________________________________________________________                   
       /                  /   -I     I \                               /   -I     I \
      /                   |   ---    --|                               |   ---    --|
     /                    |     2     2|                               |     2     2|
    /     I*x    -I*x     |    x     x |     /   -2*I*x    2*I*x\      |    x     x |
   /     e      e       I*\- e    + e  /   I*\- e       + e     /    I*\- e    + e  /
  /      ---- + ----- - ---------------- - ----------------------  - ----------------
\/        2       2            2                     2                      2
−i(eix2−e−ix2)2+−i(eix2−e−ix2)2−i(e2ix−e−2ix)2+eix2+e−ix2- \frac{i \left(e^{\frac{i}{x^{2}}} - e^{- \frac{i}{x^{2}}}\right)}{2} + \sqrt{- \frac{i \left(e^{\frac{i}{x^{2}}} - e^{- \frac{i}{x^{2}}}\right)}{2} - \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + \frac{e^{i x}}{2} + \frac{e^{- i x}}{2}} 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Compilar la expresión [src] 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(2x)+sin⁡(1x2)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(2 x \right)} + \sin{\left(\frac{1}{x^{2}} \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(1/(x^2)) + sin(2*x)) + sin(1/(x^2))
Abrimos la expresión [src] 
     ____________________________________          
    /                               /1 \       /1 \
   /  2*cos(x)*sin(x) + cos(x) + sin|--|  + sin|--|
  /                                 | 2|       | 2|
\/                                  \x /       \x /
sin⁡(1x2)+2sin⁡(x)cos⁡(x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(2*cos(x)*sin(x) + cos(x) + sin(x^(-2))) + sin(x^(-2))
Denominador racional [src] 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
sqrt(cos(x) + sin(x^(-2)) + sin(2*x)) + sin(x^(-2))
Parte trigonométrica [src] 
          _____________________________________________                 
         /                                    / 1  \            / 1  \  
        /          2/x\                  2*cot|----|       2*cot|----|  
       /   -1 + cot |-|                       |   2|            |   2|  
      /             \2/     2*cot(x)          \2*x /            \2*x /  
     /     ------------ + ----------- + --------------  + --------------
    /             2/x\           2             2/ 1  \           2/ 1  \
   /       1 + cot |-|    1 + cot (x)   1 + cot |----|    1 + cot |----|
  /                \2/                          |   2|            |   2|
\/                                              \2*x /            \2*x /
cot⁡2(x2)−1cot⁡2(x2)+1+2cot⁡(x)cot⁡2(x)+1+2cot⁡(12x2)cot⁡2(12x2)+1+2cot⁡(12x2)cot⁡2(12x2)+1\sqrt{\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} + \frac{2 \cot{\left(\frac{1}{2 x^{2}} \right)}}{\cot^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1}} + \frac{2 \cot{\left(\frac{1}{2 x^{2}} \right)}}{\cot^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1} 
     _____________________________          
    /             /1 \                  /1 \
   /  cos(x) + sin|--| + sin(2*x)  + sin|--|
  /               | 2|                  | 2|
\/                \x /                  \x /
sin⁡(1x2)+sin⁡(2x)+cos⁡(x)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
       _____________________________          
      /    1         1         1          1   
     /  ------- + -------- + ------  + -------
    /      /1 \   csc(2*x)   sec(x)       /1 \
   /    csc|--|                        csc|--|
  /        | 2|                           | 2|
\/         \x /                           \x /
1sec⁡(x)+1csc⁡(2x)+1csc⁡(1x2)+1csc⁡(1x2)\sqrt{\frac{1}{\sec{\left(x \right)}} + \frac{1}{\csc{\left(2 x \right)}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}} 
     _______________________________________               
    /             /1    pi\      /      pi\       /1    pi\
   /  cos(x) + cos|-- - --| + cos|2*x - --|  + cos|-- - --|
  /               | 2   2 |      \      2 /       | 2   2 |
\/                \x      /                       \x      /
cos⁡(x)+cos⁡(−π2+1x2)+cos⁡(2x−π2)+cos⁡(−π2+1x2)\sqrt{\cos{\left(x \right)} + \cos{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)} + \cos{\left(2 x - \frac{\pi}{2} \right)}} + \cos{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)} 
       __________________________________          
      /    1         1            1            1   
     /  ------- + -------- + -----------  + -------
    /      /1 \   csc(2*x)      /pi    \       /1 \
   /    csc|--|              csc|-- - x|    csc|--|
  /        | 2|                 \2     /       | 2|
\/         \x /                                \x /
1csc⁡(−x+π2)+1csc⁡(2x)+1csc⁡(1x2)+1csc⁡(1x2)\sqrt{\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 x \right)}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}}} + \frac{1}{\csc{\left(\frac{1}{x^{2}} \right)}} 
     __________________________________          
    /    /1 \                 /    pi\       /1 \
   /  sin|--| + sin(2*x) + sin|x + --|  + sin|--|
  /      | 2|                 \    2 /       | 2|
\/       \x /                                \x /
sin⁡(1x2)+sin⁡(2x)+sin⁡(x+π2)+sin⁡(1x2)\sqrt{\sin{\left(\frac{1}{x^{2}} \right)} + \sin{\left(2 x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}} + \sin{\left(\frac{1}{x^{2}} \right)} 
          ____________________________________________                 
         /                                   / 1  \            / 1  \  
        /         2/x\                  2*tan|----|       2*tan|----|  
       /   1 - tan |-|                       |   2|            |   2|  
      /            \2/     2*tan(x)          \2*x /            \2*x /  
     /     ----------- + ----------- + --------------  + --------------
    /             2/x\          2             2/ 1  \           2/ 1  \
   /       1 + tan |-|   1 + tan (x)   1 + tan |----|    1 + tan |----|
  /                \2/                         |   2|            |   2|
\/                                             \2*x /            \2*x /
1−tan⁡2(x2)tan⁡2(x2)+1+2tan⁡(x)tan⁡2(x)+1+2tan⁡(12x2)tan⁡2(12x2)+1+2tan⁡(12x2)tan⁡2(12x2)+1\sqrt{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{2 \tan{\left(\frac{1}{2 x^{2}} \right)}}{\tan^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1}} + \frac{2 \tan{\left(\frac{1}{2 x^{2}} \right)}}{\tan^{2}{\left(\frac{1}{2 x^{2}} \right)} + 1} 
       _______________________________________               
      /   1           1               1               1      
     /  ------ + ------------ + -------------  + ------------
    /   sec(x)      /1    pi\      /      pi\       /1    pi\
   /             sec|-- - --|   sec|2*x - --|    sec|-- - --|
  /                 | 2   2 |      \      2 /       | 2   2 |
\/                  \x      /                       \x      /
1sec⁡(2x−π2)+1sec⁡(−π2+1x2)+1sec⁡(x)+1sec⁡(−π2+1x2)\sqrt{\frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)}} + \frac{1}{\sec{\left(x \right)}}} + \frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{1}{x^{2}} \right)}} 
sqrt(1/sec(x) + 1/sec(x^(-2) - pi/2) + 1/sec(2*x - pi/2)) + 1/sec(x^(-2) - pi/2)
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